Greatest Common Factor of 972 and 978

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 972, 978 i.e. 6 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 972 and 978 is 6.

GCF(972,978) = 6

GCF of 972 and 978

Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;

GCF of:
and

Greatest Common Factor of 972 and 978

GCF of 972 and 978 is 6

Prime Factorization of 972


2 972
2 486
3 243
3 81
3 27
3 9
3 3
1

Prime factors of 972 are 2,3. Prime factorization of 972 in exponential form is:

972 = 22×35

Prime Factorization of 978


2 978
3 489
163 163
1

Prime factors of 978 are 2,3,163. Prime factorization of 978 in exponential form is:

978 = 21×31×1631

∴ So by taking common prime factors GCF of 972 and 978 is 6

Greatest Common Factor of 972 and 978 by matching factors method

Factors of 972

List of positive integer factors of 972 that divides 972 without a remainder.

1,2,3,4,6,9,12,18,27,36,54,81,108,162,243,324,486,972

Factors of 978

List of positive integer factors of 978 that divides 978 without a remainder.

1,2,3,6,163,326,489,978

Greatest Common Factor

We found the factors and prime factorization of 972 and 978. The biggest common factor number is the GCF number.
So the greatest common factor 972 and 978 is 6.

Also check out the Least Common Multiple of 972 and 978

Properties of GCF 972 and 978

(i) The GCF of 972 and 978 is associative

GCF of 972 and 978 = GCF of 978 and 972

Related Greatest Common Factor of 972

Related Greatest Common Factor of 978

Frequently Asked Questions on GCF of 972 and 978

1. What is the GCF of 972 and 978?

Answer: GCF of 972 and 978 is 6.

2. What are the Factors of 972?

Answer: Factors of 972 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, 972. There are 18 integers that are factors of 972. The greatest factor of 972 is 972.

3. What are the Factors of 978?

Answer: Factors of 978 are 1, 2, 3, 6, 163, 326, 489, 978. There are 8 integers that are factors of 978. The greatest factor of 978 is 978.

4. How to Find the GCF of 972 and 978?

Answer:

Greatest Common Factor of 972 and 978 = 6

Step 1: Find the prime factorization of 972

972 = 2 x 2 x 3 x 3 x 3 x 3 x 3

Step 2: Find the prime factorization of 978

978 = 2 x 3 x 163

Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:

GCF = 2 x 3 = 6

Step 4: Therefore, the greatest common factor of 972 and 978 is 6